Exponent dependence measures of survival functions and correlated frailty models

TL;DR

This paper explores the use of exponent measures in survival functions and their relation to copula dependence models, frailty models, and Lévy measures, providing a semiparametric framework with detailed examples.

Contribution

It introduces a semiparametric approach linking survival functions, copulas, and exponent measures, with detailed constructions and illustrations of higher-order dependencies.

Findings

Connection between survival functions and exponent measures.

Linkage of frailty models to copulas and Lévy measures.

Comprehensive examples and graphical illustrations.

Abstract

The present article studies survival analytic aspects of semiparametric copula dependence models with arbitrary univariate marginals. The underlying survival functions admit a representation via exponent measures which have an interpretation within the context of hazard functions. In particular, correlated frailty survival models are linked to copulas. Additionally, the relation to exponent measures of minumum-infinitely divisible distributions as well as to the L\'evy measure of the L\'evy-Khintchine formula is pointed out. The semiparametric character of the current analyses and the construction of survival times with dependencies of higher order are carried out in detail. Many examples including graphics give multifarious illustrations.